python code to find inverse of a matrix without numpy

The following example checks that a * a+ * a == a and Example 1: Python import numpy as np We start with the A and I matrices shown below. I know that feeling youre having, and its great! We will also go over how to use numpy /scipy to invert a matrix at the end of this post. Compute the (Moore-Penrose) pseudo-inverse of a matrix. The function takes a square matrix as input and returns a square matrix as output. It generously provides a very good explanation of how the process looks like "behind the scenes". Singular values less than or equal to Lets first introduce some helper functions to use in our notebook work. When you are ready to look at my code, go to the Jupyter notebook called MatrixInversion.ipynb, which can be obtained from the github repo for this project. Of course, in that file there are still numpy function used, so if you want to implement with no numpy at all, you have to implement every called functions in that file. I do love Jupyter notebooks, but I want to use this in scripts now too. Compare the predicted values from the IDW interpolation to the known values in the external dataset and calculate error metrics. Which ability is most related to insanity: Wisdom, Charisma, Constitution, or Intelligence? | Introduction to Dijkstra's Shortest Path Algorithm. The inverse of a matrix is that matrix which, when multiplied with the original matrix, results in an identity matrix. There's a Jupyter notebook as well, btw. You can use the results for further spatial analysis or create maps to visualize and communicate your findings. So. \(A^+ = Q_2 \Sigma^+ Q_1^T\), where \(Q_{1,2}\) are It is remarkable that the humans when picking an example of a matrix so often manage to pick a singular matrix! This is often unnecessary and can be numerically unstable. The only really painful thing about this method of inverting a matrix, is that, while its very simple, its a bit tedious and boring. In this blog post, we delve into the fundamentals of IDW interpolation, exploring its underlying assumptions, key parameters, and the factors that impact its performance. Figure 1 depicts the step-by-step operations necessary to alter the first three columns of the augmented matrix to achieve rref. Use the numpy.matrix Class to Find the Inverse of a Matrix in Python Use the scipy.linalg.inv () Function to Find the Inverse of a Matrix in Python Create a User-Defined Function to Find the Inverse of a Matrix in Python A matrix is a two-dimensional array with every element of the same size. Since the resulting inverse matrix is a $3 \times 3$ matrix, we use the numpy.eye() function to create an identity matrix. Thanks for contributing an answer to Stack Overflow! Making statements based on opinion; back them up with references or personal experience. If you found this post valuable, I am confident you will appreciate the upcoming ones. When what was A becomes an identity matrix, I will then be A^{-1}. When a gnoll vampire assumes its hyena form, do its HP change? Matrix or stack of matrices to be pseudo-inverted . In case youve come here not knowing, or being rusty in, your linear algebra, the identity matrix is a square matrix (the number of rows equals the number of columns) with 1s on the diagonal and 0s everywhere else such as the following 33 identity matrix. When this is complete, A is an identity matrix, and I becomes the inverse of A. Lets go thru these steps in detail on a 3 x 3 matrix, with actual numbers. Create the augmented matrix using NumPys column-wise concatenation operation as given in Gist 3. Comment if you have any doubts or suggestions regarding this article. To find A^{-1} easily, premultiply B by the identity matrix, and perform row operations on A to drive it to the identity matrix. There are also some interesting Jupyter notebooks and .py files in the repo. It assumes that the influence of a data point decreases with increasing distance from the unmeasured location. Making statements based on opinion; back them up with references or personal experience. Changed in version 1.14: Can now operate on stacks of matrices. It's more efficient and more accurate to use code that solves the equation Ax = b for x directly than to calculate A inverse then multiply the inverse by B. Parameters: a(, M, M) array_like Matrix to be inverted. Install the required libraries (if not already installed): Create a Python script or a Jupyter Notebook and import the necessary libraries: Define a function to perform IDW interpolation: Load your data (e.g., using pandas) and prepare the input arrays: Perform IDW interpolation and process the results: Define the spatial extent and create a grid for the unknown points: Process the results and visualize or export them as needed. Using the steps and methods that we just described, scale row 1 of both matrices by 1/5.0, 2. Divide your dataset into a training set and a validation set (e.g., 70% training, 30% validation). Never used R, but why would an external program and its python binder be better than the most well known scientific package of python? This article outlined an essential method used in matrix algebra to compute the inverse of a matrix. To inverse a matrix place it as a 2D array and then run the Inverse function, Inverse matrix of 3x3 without numpy [python3]. Broadcasts against the stack of matrices. IDW has been widely used in various fields, including environmental sciences, geosciences, and agriculture, to create continuous surfaces from point data. Can my creature spell be countered if I cast a split second spell after it? As previously stated, we make copies of the original matrices: Lets run just the first step described above where we scale the first row of each matrix by the first diagonal element in the A_M matrix. Proper way to declare custom exceptions in modern Python? Im Andy! I wish I could upvote more than once, @stackPusher I am getting this error on your code. Discard data in a (may improve performance). It introduces a method to find an inverse matrix using row reduction. Generating points along line with specifying the origin of point generation in QGIS, Vector Projections/Dot Product properties. Increasing the size of the matrix is also possible. numpy.linalg.pinv #. Why is reading lines from stdin much slower in C++ than Python? The inverse matrix can be used to solve the equation A x = b by adding it to each term: A 1 A x = A 1 b Since we know by definition that A 1 A = I, we have: I n x = A 1 b We saw that a vector is not changed when multiplied by the identity matrix. This article teaches you how you can do matrix inversion without the use of NumPy in Python. a+ * a * a+ == a+: Mathematical functions with automatic domain. It also raises an error if a singular matrix is used. Scale row 3 of both matrices by 1/3.667, 8. Check out my other articles if you are interested in Python, engineering, and data science. We and our partners use cookies to Store and/or access information on a device. Why don't we use the 7805 for car phone chargers? How to Compute the Inverse Cosine and Inverse Hyperbolic Cosine in PyTorch, Compute the inverse of a matrix using NumPy, Compute the inverse sine with scimath using NumPy in Python, Difference between Numpy array and Numpy matrix, How to compute the inverse of a square matrix in PyTorch, Natural Language Processing (NLP) Tutorial, Introduction to Heap - Data Structure and Algorithm Tutorials, Introduction to Segment Trees - Data Structure and Algorithm Tutorials. Follow these steps to perform IDW interpolation in R: Here, replace x and y with the column names of the spatial coordinates in your data. The numpy.linalg.inv () function computes the inverse of a matrix. A minor scale definition: am I missing something? According to the requirement, should be the accepted answer. What were the most popular text editors for MS-DOS in the 1980s? What positional accuracy (ie, arc seconds) is necessary to view Saturn, Uranus, beyond? A=\begin{bmatrix}5&3&1\\3&9&4\\1&3&5\end{bmatrix}\hspace{5em} I=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}. How do I get the inverse of a matrix in python? Doing so gives us matrix([[ 0.3, -0.2],[-0.7, 0.8]]) as the inverse matrix. A_M and I_M , are initially the same, as A and I, respectively: A_M=\begin{bmatrix}5&3&1\\3&9&4\\1&3&5\end{bmatrix}\hspace{4em} I_M=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}, 1. Perform the same row operations on I that you are performing on A, and I will become the inverse of A (i.e. @MohanadKaleia you're right, thanks. We can use NumPy to easily find out the inverse of a matrix. rcond * largest_singular_value are set to zero. Subtract -0.083 * row 3 of A_M from row 1 of A_M Subtract -0.083 * row 3 of I_M from row 1 of I_M, 9. The code in Gist 6 is a simple method to record the timings. Product of a square matrix A with its adjoint yields a diagonal matrix, where each diagonal entry is equal to determinant of A.i.e. Inverse distance weighting in QGIS. Please feel free to ask any questions. Without accounting for certain edge cases, the code provided below in Gist 4 is a naive implementation of the row operations necessary to obtain A inverse. A must be square (nn) and have a non-zero determinant. But what if we want to calculate it without using NumPy? We can also use the numpy.matrix class to find the inverse of a matrix. Several validation techniques can be used to assess the accuracy: This technique involves iteratively removing one data point from the dataset, performing IDW interpolation without that point, and comparing the predicted value at the removed points location to its true value. By using our site, you I love numpy, pandas, sklearn, and all the great tools that the python data science community brings to us, but I have learned that the better I understand the principles of a thing, the better I know how to apply it. Your home for data science. Note that getMatrixInverse(m) takes in an array of arrays as input. On the ubuntu-kubuntu platform, the debian package numpy does not have the matrix and the linalg sub-packages, so in addition to import of numpy, scipy needs to be imported also. rev2023.4.21.43403. Among these techniques, Inverse Distance Weighting (IDW) stands out for its simplicity and ease of implementation. What is Wario dropping at the end of Super Mario Land 2 and why? An example of data being processed may be a unique identifier stored in a cookie. The inverse of a matrix is such that if it is multiplied by the original matrix, it results in identity matrix. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. Compute the (multiplicative) inverse of a matrix. Also, IX=X, because the multiplication of any matrix with an identity matrix leaves it unaltered. The way that I was taught to inverse matrices, in the dark ages that is, was pure torture and hard to remember! What "benchmarks" means in "what are benchmarks for?". For those like me, who were looking for a pure Python solution without pandas or numpy involved, check out the following GitHub project: https://github.com/ThomIves/MatrixInverse. Is this plug ok to install an AC condensor? If the diagonal terms of A are multiplied by a large enough factor, say 2, the matrix will most likely cease to be singular or near singular. This is just a high level overview. Can you please see.. in getMatrixMinor(m, i, j) 3 4 def getMatrixMinor(m,i,j): ----> 5 return [row[:j] + row[j+1:] for row in (m[:i]+m[i+1:])] 6 7 def getMatrixDeternminant(m): ValueError: operands could not be broadcast together with shapes (0,172877) (172876,172877), If you're using python3, then you need to define. Doing such work will also grow your python skills rapidly. In this video, I create a series of functions to find the inverse of a matrix.NOTE: You may notice a few inconsistencies throughout the video. These functions will be used in a function that will return the final inverse. I hope that you will make full use of the code in the repo and will refactor the code as you wish to write it in your own style, AND I especially hope that this was helpful and insightful. This can lead to biased results if the underlying data exhibit strong spatial autocorrelation. We can use the scipy module to perform different scientific calculations using its functionalities. Plus, tomorrows machine learning tools will be developed by those that understand the principles of the math and coding of todays tools. For this, we will use a series of user-defined functions. Employ the outlined theoretical matrix algebraic method and the equivalent Python code to understand how the operation works. To perform IDW interpolation in QGIS, follow the steps below: Now you have successfully performed IDW interpolation in QGIS. Remember that the accuracy and quality of the IDW interpolation results depend on the characteristics and distribution of the point data. The other sections perform preparations and checks. Please refer https://www..geeksforgeeks.org/determinant-of-a-matrix/ for details of getCofactor() and determinant(). Essentially, multiplying a matrix by its inverse gives the Identity Matrix, I, as indicated by Equation 1. Create an augmented matrix from the components of Equation 3. If at this point you see enough to muscle through, go for it! Calculate the generalized inverse of a matrix using its The above example returns a nested list that represents the given matrixs inverse. But inv (A).A=I, the identity matrix. Consider a typical linear algebra problem, such as: We want to solve for X, so we obtain the inverse of A and do the following: Thus, we have a motive to find A^{-1}. Subtract 3.0 * row 1 of A_M from row 2 of A_M, and Subtract 3.0 * row 1 of I_M from row 2 of I_M, 3. If you would like to change your settings or withdraw consent at any time, the link to do so is in our privacy policy accessible from our home page.. QGIS includes the Inverse Distance Weighting (IDW) interpolation technique as one of its core features. FL, Academic Press, Inc., 1980, pp. Does a password policy with a restriction of repeated characters increase security? The second matrix is of course our inverse of A. Data Scientist, PhD multi-physics engineer, and python loving geek living in the United States. See if you can code it up using our matrix (or matrices) and compare your answer to our brute force effort answer. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. #. This function raises an error if the inverse of a matrix is not possible, which can be because the matrix is singular. Suspendisse pellentesque sem metus, et mollis purus auctor in eoses eget. Therefore, using this function in a try and except block is recommended. Inverse Distance Weighting (IDW) is an interpolation technique commonly used in spatial analysis and geographic information systems (GIS) to estimate values at unmeasured locations based on the values of nearby measured points. Review the article below for the necessary introduction to Gaussian elimination. PLEASE NOTE: The below gists may take some time to load. This way X can be found by multiplying B with the inverse of matrix A. Using the Gauss-Jordan method to find the inverse of a given matrix in Python. Does the 500-table limit still apply to the latest version of Cassandra? It's best to use this. Python provides a very easy method to calculate the inverse of a matrix. G. Strang, Linear Algebra and Its Applications, 2nd Ed., Orlando, So how do we easily find A^{-1} in a way thats ready for coding? Note that all the real inversion work happens in section 3, which is remarkably short. Ha! \(Ax = b\), i.e., if \(\bar{x}\) is said solution, then Now that you have learned how to calculate the inverse of the matrix, let us see the Python code to perform the task: In the above code, various functions are defined. So we get, X=inv (A).B. There's no python "builtin" doing that for you and programming a matrix inversion yourself is anything but easy (see e.g. Probably not. To view the purposes they believe they have legitimate interest for, or to object to this data processing use the vendor list link below. With numpy.linalg.inv an example code would look like that: import numpy as np M = np.array ( [ [1,0,0], [0,1,0], [0,0,1]]) Minv = np.linalg.inv (M) python matrix numba inverse Share Improve this question Follow edited Jan 18, 2019 at 19:01 cs95 371k 94 684 736 asked Aug 20, 2015 at 9:06 Alessandro Vianello 437 2 6 9 1 Probably not. Find centralized, trusted content and collaborate around the technologies you use most. He is an avid learner who enjoys learning new things and sharing his findings whenever possible. All those python modules mentioned above are lightening fast, so, usually, no. "Least Astonishment" and the Mutable Default Argument. Or, as one of my favorite mentors would commonly say, Its simple, its just not easy. Well use python, to reduce the tedium, without losing any view to the insights of the method. This command expects an input matrix and a right-hand side vector. How to do gradient descent in python without numpy or scipy. #. Does a password policy with a restriction of repeated characters increase security? A matrix is a two-dimensional array with every element of the same size. Compute the inverse of a matrix. Great question. I have interests in maths and engineering. Compute the (Moore-Penrose) pseudo-inverse of a Hermitian matrix. Syntax: numpy.linalg.inv(a) Parameters: a: Matrix to be inverted Returns: Inverse of the matrix a. You should have a look at numpy if you do matrix manipulation. In this Python Programming video tutorial you will learn how to inverse a matrix using NumPy linear algebra module in detail.NumPy is a library for the Pyth. Obtain inverse matrix by applying row operations to the augmented matrix. Subtract 0.472 * row 3 of A_M from row 2 of A_M Subtract 0.472 * row 3 of I_M from row 2 of I_M. orthogonal matrices, \(\Sigma\) is a diagonal matrix consisting I kept getting interrupted as I recorded the video, so I have to restart or restate some parts.Also, it was only after I finished recording everything that I realized I forgot to increase the font size of the code. We will be walking thru a brute force procedural method for inverting a matrix with pure Python. To perform IDW interpolation in QGIS, follow the steps below: Load the point data: Add the point data layer you want to interpolate to your project by clicking on "Layer" > "Add Layer" > "Add . Content Discovery initiative April 13 update: Related questions using a Review our technical responses for the 2023 Developer Survey. @stackPusher this is tremendous. Equation 3 is equivalent to Equation 1, with the variables substituted. That was the reason I made this as well. We are going to make use of array () method from Numpy to create a python matrix. Would I recommend that you use what we are about to develop for a real project? Think of the inversion method as a set of steps for each column from left to right and for each element in the current column, and each column has one of the diagonal elements in it,which are represented as the S_{k1} diagonal elements where k=1\, to\, n. Well start with the left most column and work right. Here are some ways to extract point data from line or polygon layers: Once you have a point layer, you can perform IDW interpolation in QGIS using the Interpolation plugin (Raster > Interpolation > Interpolation) or the IDW interpolation tool in the Processing Toolbox (Interpolation > IDW interpolation). You dont need to use Jupyter to follow along. Define A from Equation 2 as a NumPy array using Gist 1. It's generally better as a programmer to use library code written by numerical mathematics experts, unless you are willing to spend time understanding the physical and mathematical nature of the particular problem that you are addressing and become your own mathematics expert in your own specialist field. More advanced interpolation methods, such as kriging or spline interpolation, may provide more accurate results in certain cases. Using determinant and adjoint, we can easily find the inverse of a square matrix using the below formula. value decomposition of A, then Is this plug ok to install an AC condensor? You can verify the result using the numpy.allclose() function. The inverse of a matrix is that matrix which when multiplied with the original matrix will give as an identity matrix. Gist 5 provides the code to create a random square matrix in NumPy. After youve read the brief documentation and tried it yourself, compare to what Ive done below: Notice the round method applied to the matrix class. Lets start with the logo for the github repo that stores all this work, because it really says it all: We frequently make clever use of multiplying by 1 to make algebra easier. \(A^+\) is that matrix such that \(\bar{x} = A^+b\). With numpy.linalg.inv an example code would look like that: Here is a more elegant and scalable solution, imo. In such cases, you may want to explore other interpolation methods or spatial analysis techniques more suited to your data type and application. The only minor change required is in. zeros), and then \(\Sigma^+\) is simply the diagonal matrix Thus, a statement above bears repeating: tomorrows machine learning tools will be developed by those that understand the principles of the math and coding of todays tools. One way to multiply by 1 in linear algebra is to use the identity matrix. Given a square matrix a, return the matrix ainv satisfying dot (a, ainv) = dot (ainv, a) = eye (a.shape [0]). Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Quisque imperdiet eros leo, eget consequat orci viverra nec. numpy.linalg.inv () We use numpy.linalg.inv () function to calculate the inverse of a matrix. However, if the determinant of the input matrix is zero, it gives an error message and returns None. Connect and share knowledge within a single location that is structured and easy to search. This seems more efficient than stackPusher's answer, right? NumPy is over a second quicker to invert the matrix. Or just calculate the det outside the Numba function and pass it as an argument, cg.info.hiroshima-cu.ac.jp/~miyazaki/knowledge/teche0023.html, http://cg.info.hiroshima-cu.ac.jp/~miyazaki/knowledge/teche23.html, How a top-ranked engineering school reimagined CS curriculum (Ep. Inverse of a matrix in Python In order to calculate the inverse matrix in Python we will use the numpy library. If you go about it the way that you would program it, it is MUCH easier in my opinion. LinearAlgebraPurePython.py is a module file to be imported and have it's functions called in basic linear algebra work. In fact just looking at the inverse gives a clue that the inversion did not work correctly. Of course one needs to write another 'brute force' implementation for the determinant calculation as well. This article follows Gaussian Elimination Algorithm in Python. consisting of the reciprocals of As singular values Find the determinant of each of the 22 minor matrices. By using our site, you Using Numpy For The Above Operations A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. However, if you have other types of spatial data, such as lines or polygons, you can still use IDW interpolation by extracting point data from these layers. The getMatrixInverse() function calculates and returns the inverse of the matrix. Finding the inverse matrix of a 2x2 matrix is relatively easy. Whether to check that the input matrix contains only finite numbers. Published by Thom Ives on November 1, 2018November 1, 2018. IDW does not account for spatial autocorrelation (i.e., the degree to which neighboring points are correlated). LinearAlgebraPractice.py is a simple python script that imports LinearAlgebraPurePython.py and uses it's functions. If you get stuck, take a peek, but it will be very rewarding for you if you figure out how to code this yourself. What if my matrix members are exact rationals? If you did most of this on your own and compared to what I did, congratulations! Lets first define some helper functions that will help with our work. For small matrices it is particularly fast: Notice that the speedup only works for NumPy inverse, not SciPy (as expected). But it is remarkable that python can do such a task in so few lines of code. It seems like that avoid the accuracy problem, although of course at the cost of making the performance problem a lot worse. If available, use an independent dataset with known values to validate the accuracy of your IDW interpolation results. Python makes use of the NumPy module, which is an abbreviation for Numerical Python, in dealing with matrices and arrays in Python. You can further process the results, visualize them using libraries like Matplotlib, or export them to a file. Gist 1 Define A using Numpy Similarly, instantiate a new variable I, which is the same square shape as A. QGIS includes the Inverse Distance Weighting (IDW) interpolation technique as one of its core features. Ive also saved the cells as MatrixInversion.py in the same repo. Consider two given matrixes A and B and an unknown matrix X in the form AX=B. Its interesting to note that, with these methods,a function definition can be completed in as little as 10 to 12 lines of python code. Why wouldnt we just use numpy or scipy? Comparing the runtime for the custom algorithm versus the NumPy equivalent highlights the speed difference. The inverse of a matrix exists only if the matrix is non-singular i.e., determinant should not be 0. [1] Matrix Algebra for Engineers Jeffrey R. Chasnov. However, libraries such as NumPy in Python are optimised to decipher inverse matrices efficiently. This type of effort is shown in the ShortImplementation.py file. The inversion of a matrix is useful in solving a system of linear equations. Content Discovery initiative April 13 update: Related questions using a Review our technical responses for the 2023 Developer Survey, How to solve the inverse square of a matrix without using numpy's solver, ValueError: operands could not be broadcast together with shapes (5,) (30,), Compute matrix inverse with decimal object. When we are on a certain step, S_{ij}, where i \, and \, j = 1 \, to \, n independently depending on where we are at in the matrix, we are performing that step on the entire row and using the row with the diagonal S_{k1} in it as part of that operation. The shortest possible code is rarely the best code. To learn more, see our tips on writing great answers. Its particularly useful when working with spatially distributed data, such as climate variables, elevation, or pollution levels. If a is a matrix instance, then so We can represent matrices using numpy arrays or nested lists. The numpy module has different functionalities to create and manipulate arrays in Python. However, compared to the ancient method, its simple, and MUCH easier to remember. Success! Also, once an efficient method of matrix inversion is understood, you are ~ 80% of the way to having your own Least Squares Solver and a component to many other personal analysis modules to help you better understand how many of our great machine learning tools are built. NOTE: The last print statement in print_matrix uses a trick of adding +0 to round(x,3) to get rid of -0.0s. Well do a detailed overview with numbers soon after this. Returns: ainv(, M, M) ndarray or matrix (Multiplicative) inverse of the matrix a. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide. IDW is a relatively simple and intuitive method for spatial interpolation, and its results can be easily visualized using contour maps or heat maps. This is because it has been deprecated and ambiguous while working with numpy arrays. Adjoint (or Adjugate) of a matrix is the matrix obtained by taking the transpose of the cofactor matrix of a given square matrix is called its Adjoint or Adjugate matrix. C++ program to construct an expression tree, Python program to Sort elements by frequency, Convert double number to 3 decimal places number in C++, Auto scroll to a specific position in SwiftUI, Scroll to a specific position in SwiftUI with button click, Python program to find the smallest number in a NumPy array. This means that IDW might not be suitable for non-stationary data, where the relationship between the variable of interest and distance changes across space. Inverse is used to find the solution to a system of linear equations. I dont recommend using this. Please write comments if you find anything incorrect, or if you want to share more information about the topic discussed above. Is there a way to efficiently invert an array of matrices with numpy? You could calculate the determinant of the matrix which is recursive of As so-called singular values, (followed, typically, by See the code below. I found that Gaussian Jordan Elimination Algorithm helped a lot when attempting this. For a 4 x 4 matrix it's probably just about OK to use the mathematical formula, which you can find using Googling "formula for 4 by 4 matrix inverse". Read the comments or function definitions to understand what each function does. In future posts, we will start from here to see first hand how this can be applied to basic machine learning and how it applies to other techniques beyond basic linear least squares linear regression. Lets simply run these steps for the remaining columns now: That completes all the steps for our 55. Here are the steps, S, that wed follow to do this for any size matrix. Using determinant and adjoint, we can easily find the inverse of a square matrix using the below formula, If det (A) != 0 A -1 = adj (A)/det (A) Else "Inverse doesn't exist" In general inverting a general matrix is not for the faint-hearted. What are the advantages and limitations of IDW compared to other interpolation methods?

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